We explore the morphogenesis of Ammonites’ seashells in our paper

“Morphomechanics and developmental constraints
in the evolution of ammonites shell form”

submitted for publication in Journal of Experimental Zoology Part B: Molecular and Developmental Evolution. This article is a collaboration between Alexander Erlich, Alain Goriely and Derek Moulton from the University of Oxford, and Régis Chirat from Université Lyon 1. We develop a model which allows us to re-interpret and add insights into the morphology of the beautiful spiral coiling and oscillatory ribbing pattern of the seashells in the light of mechanics and homeostasis. Based on fundamental principles of growth and elasticity, we established a mechanical basis for the relationships between the spiral-shaped coiling pattern, the oscillatory ribbing pattern and elliptic cross-section shape of the shells. Specifically, we model the stretching, bending and active growth of the soft shell-generating organ. This model is consistent with and provides a mechanical basis for Buckman’s Law, which is a gold standard collection of rules about the relationship of geometry and ribbing observed in Ammonite’s shells. To better illustrate the results of this model, we developed a supplementary interactive real-time simulation of the seashell 3D surfaces, which you can download for the operating system of your choice.

Run in browser

(no STL export)


Windows (64bit)


Mac (Universal)


Linux (Universal)

The simulation has an option to generate an STL file of the shell you are viewing. We also provide a Mathematica notebook which can be used to better understand the model and to plot the 3D surfaces. Below is a phtograph of a real-life Ammonite, a 3D print made as an output of our model, and a computer generated image of the underlying 3D surface which will be immediately visible when the above simulation is loaded.

The details about the biological motivation, mechanical details, and computational realisation (as well as meaning of the model parameters manipulated in the simulation) are discussed in detail in our paper.